{ "category": "Statistical functions", "display_name": "MIN", "entry_kind": "built_in_function", "eval_api": { "method": "POST", "url": "https://handbook.dnacalc.com/api/eval" }, "function_id": "FUNC.MIN", "implementation_state": { "answer_bank": { "excel_builds": [ "20430" ], "larger_numeric": 0, "last_bit": 0, "matched": 1212, "other_mismatch": 0, "refused": 0, "rows": 1212, "unread": 0, "worst_ulp": 0 }, "detail": "Recorded: 1,212 in the answer bank and 18 workbook cells.", "dnacalc_commit": "9e1884369a678158dd82d3d74188daf986995e87", "in_catalogue": true, "state": "matches", "state_label": "Matches every recorded Excel answer", "summary": "Matches all 1,230 recorded answers", "workbook_corpus": { "cells": 19, "matched": 18, "pending": 1 } }, "implementations": [ { "commit": "9e1884369a678158dd82d3d74188daf986995e87", "flavour": "excel-compatibility-candidate", "language": "Rust", "name": "CalcFunc", "own_code": [ "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/aggregate.rs#L113-L113" ], "repository": "https://github.com/DnaCalc/DnaCalc", "shared_code": [ "catalogue/aggregate::aggregate", "catalogue/aggregate::min", "catalogue/aggregate::extreme", "catalogue/aggregate::holds_held_arrays", "catalogue/aggregate::read_held_references", "catalogue/aggregate::number_of", "catalogue/aggregate::each_value", "catalogue/aggregate::read_values", "catalogue/aggregate::reader", "catalogue/aggregate::read_reference", "catalogue/comparison::overflow_numbers", "catalogue/comparison::numbers", "catalogue/comparison::in_band", "catalogue/comparison::Rounded::up", "catalogue/comparison::Roundings::of", "catalogue/comparison::Roundings::disjoint", "decimal::low32", "decimal::Natural::from_u64", "decimal::Natural::pow10", "decimal::Natural::normalize", "decimal::Natural::is_zero", "decimal::Natural::mul_add_small", "decimal::Natural::times_pow10", "decimal::Natural::times_pow5", "decimal::Natural::times_pow2", "decimal::ExactDecimal::binary" ], "source": "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/aggregate.rs#L113-L113", "state": "matches", "suite": null, "summary": "Matches all 1,230 recorded answers" } ], "json_url": "https://handbook.dnacalc.com/api/functions/FUNC.MIN.json", "name": "MIN", "notes": [], "schema": "efh.function-reference/v1", "section_order": [ "what-it-does", "try-it", "quirks", "how-to-implement", "version-differences", "alternatives" ], "sections": { "alternatives": "\n### Relationships\n\n\n- **[MAX](FUNC.MAX.md)** — the exact mirror. Same argument shape, same documented coercion\n table, same documented `0`. Any behavioural difference beyond the comparator is a defect in\n one of them, which makes cross-testing the pair unusually productive.\n- **[MINA](FUNC.MINA.md)** — the variant counting text and logicals in references, named by\n `MIN`'s own documentation. On `MINA` the zero-conversion trap is at its worst: any text in an\n all-positive column pulls the minimum to `0`.\n- **[MINIFS](FUNC.MINIFS.md)** — the conditional form, which returns `0` when nothing matches —\n the same convention, with the same all-positive-data hazard.\n- **[SMALL](FUNC.SMALL.md)** — the general order-statistic selector; `SMALL(array, 1)` is the\n minimum over the same admitted set, but `SMALL` errors on an empty array instead of returning\n zero. The `MIN`/`SMALL` pair is the cleanest illustration of two functions computing the same\n thing with different empty-set conventions, and `SMALL` is the safer of the two when \"no\n data\" must not be confused with \"zero\".\n- **[DMIN](FUNC.DMIN.md)** — the database-family minimum with criteria-range selection.\n- **[SUBTOTAL](FUNC.SUBTOTAL.md)** (function numbers 5 and 105) and\n **[AGGREGATE](FUNC.AGGREGATE.md)** (function number 5) — the filter-aware and error-skipping\n minima. `AGGREGATE` is the only route to a minimum that ignores error values.\n- **Confused with:** `MIN` and `SMALL` on ranges containing text (same scan policy, so they\n should agree); and with the belief that an empty `MIN` is an error, which the documentation\n contradicts.\n\n\n", "how-to-implement": "\n### Numerical notes\n\n\n`MIN` has no arithmetic and therefore no rounding error. Three questions remain, and all three\nare about definition.\n\n**1. The comparison predicate.** A minimum needs a total order. IEEE-754 `<` is one on the\ndoubles Excel can hold, except that `+0` and `−0` compare equal; Excel has no NaN in its\npublished value universe, so the NaN-poisoning problem does not arise at this level. Whether\nExcel's `MIN` uses raw `<` or the tolerant truncation-style 15-significant-digit comparison it\napplies in some other families is open. The consequence is limited to which of two equal-\ncomparing representations is returned, but it is observable.\n\n**3. The empty-set identity.** Mathematically `min ∅ = +∞`, which Excel cannot represent, so\nthe specification substitutes `0`. As argued above, the substitution is directional in its\nharm: `0` is a *lower* bound for most real spreadsheet data, so an empty `MIN` does not merely\ngive a wrong answer, it gives an answer that dominates every correct one downstream.\n\nFor an implementer, the rule follows directly: initialise with a **found flag** plus a\nsentinel, never with `0` and never with `f64::INFINITY` alone. `0` is wrong for all-positive\ndata; `+∞` produces a value outside Excel's value universe. Track \"have I seen a number\"\nseparately from \"what is the best so far\", and apply the documented zero only at the end. The\nsame advice appears on [MAX](FUNC.MAX.md) and is worth repeating because the two functions are\nusually implemented by the same person on the same afternoon and the mirror case is easy to\nget subtly different.\n\n\n", "quirks": "\n### The two coercion policies\n\n\nQuoted from Microsoft's `MIN` page, which states the split in consecutive sentences:\n\n- \"Arguments can either be numbers or names, arrays, or references that contain numbers.\"\n- \"Logical values and text representations of numbers that you type directly into the list of\n arguments are counted.\"\n- \"If an argument is an array or reference, only numbers in that array or reference are used.\n Empty cells, logical values, or text in the array or reference are ignored.\"\n- \"If the arguments contain no numbers, MIN returns 0.\"\n- \"Arguments that are error values or text that cannot be translated into numbers cause\n errors.\"\n\nAs a table:\n\n| Value | Typed **directly** into the argument list | Reached inside an **array or reference** |\n|---|---|---|\n| Number | counted | counted |\n| `TRUE` / `FALSE` | counted (as 1 / 0) | **ignored** |\n| Text that reads as a number | counted | **ignored** |\n| Text that does not read as a number | **error** | ignored |\n| Empty cell | — | ignored |\n| Error value | error | error |\n\nThis is word-for-word the [MAX](FUNC.MAX.md) table with the comparator reversed, which is how\nit should be: the two functions are documented to differ in nothing but direction. Microsoft's\npage names the same remedy for wanting more values counted: \"If you want to include logical\nvalues and text representations of numbers in a reference as part of the calculation, use the\nMINA function.\" See [MINA](FUNC.MINA.md), and read its rules before switching.\n\n\n\n### Result and edge cases\n\n\nReturns `Number`.\n\n- **No numbers among the arguments.** Microsoft documents: \"If the arguments contain no\n numbers, MIN returns 0.\" So `MIN` over a wholly blank range is documented to be `0`.\n\n **Why it matters more on `MIN` than on `MAX`.** The documented `0` is not below the data; it\n is inside the plausible range. On all-**positive** data — prices, distances, durations,\n counts, every quantity a spreadsheet is usually full of — an empty range makes `MIN` return\n `0`, which is smaller than every real value and therefore wins every subsequent comparison.\n A minimum-of-minimums over several columns reports `0` the moment one column is empty. The\n symmetric failure for `MAX` needs all-negative data, which is rarer. `MIN(MIN(A), MIN(B)) ≠\n MIN(A ∪ B)` whenever one side is empty and the other is entirely positive, and that is the\n common case rather than the exotic one.\n\n- **A single value.** `MIN(x)` is `x`, for the largest finite double and the smallest subnormal\n alike.\n- **`+0` and `−0`** compare equal under IEEE, so which representation is returned is\n unspecified and observable through `1/MIN(...)`. Unverified.\n- **Arrays** are consumed by scanning, not lifted elementwise.\n- **Dates and times** are numbers wearing formats, so `MIN` over a date column is the earliest\n date.\n\n\n\n### Errors\n\nThere is no documented `#NUM!` or `#N/A` condition, and no documented empty-input error — the\ndocumented empty-input answer is `0`.\n\n\n", "sources": "- Handbook [MAX](FUNC.MAX.md) — the mirror surface and the shared empty-set divergence finding.\n- Handbook [The value universe](../model/01-value-universe.md) — the absence of infinities from\n the published value gamut.\n- Handbook projections `data/functions/FUNC.MIN.json` (arity 1–255, `xlfMin` code 6,\n `AggregateDirectAndRangeDualPolicy`, `ReductionFold`, `SequentialLeftFold`,\n `CanonicalExcelLegacy` error algebra) and `data/presence/FUNC.MIN.json` (module `min_fn.rs`,\n unshared, no defect stream named).\n\n", "version-differences": "The recorded environments below distinguish a reading from a same-input comparison. Counts describe captured inputs in each environment; overlapping captures and comparisons are not totals of unique worksheet calls.\n\n| Excel 16.0 build | Platform and CPU | Captured inputs |\n|---|---|---:|\n| 20430 | Windows, 64-bit, CPU not recorded | 1,212 |\n\nThe record contains no same-input comparison between these environments. Reading different inputs on different builds does not establish either a version change or cross-build agreement.\n\n[Recorded environments and comparison details](https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.MIN.json).", "what-it-does": "\n`MIN(number1, [number2], …)` returns the smallest of the numeric values it admits.\n\nMathematically this is the bottom order statistic `x₍₁₎ = min{x₁ … xₙ}` — the infimum of a\nfinite set, attained, and therefore one of the inputs. `MIN` is a **selector**: it performs no\narithmetic, introduces no rounding error, and returns bits it was given.\n\n`min` is associative, commutative and idempotent with identity `+∞`, so it is a monoid fold —\nand, as with [MAX](FUNC.MAX.md), the identity is the one thing Excel cannot represent, so the\nspecification substitutes a value. Microsoft's choice is `0`, and on `MIN` that choice is more\nconsequential than on `MAX`; see below.\n\n\n### Arguments\n\n\n| Argument | Meaning | Notes |\n|---|---|---|\n| `number1` | The first value | See the note below |\n| `number2, …` | Further values | Optional |\n\nMicrosoft's page states: \"Number1 is optional, subsequent numbers are optional. 1 to 255\nnumbers for which you want to find the minimum value.\"\n\nArgument boundaries carry no meaning: `MIN(A1:A10)`, `MIN(A1:A5, A6:A10)` and\n`MIN(A1, …, A10)` all reduce over one pooled set.\n\n\n" }, "signature": { "display": "MIN(number1, [number2], ...)", "parameters": [ { "description": null, "name": "number1", "optional": false, "repeats": false }, { "description": null, "name": "number2", "optional": true, "repeats": true } ], "trailing_repeats": true }, "sources": { "metadata": { "admission": { "label": "implemented", "reason": null }, "arity": { "max": 255, "min": 1 }, "category": "Statistical functions", "classification": { "arg_preparation_profile": "ValuesOnlyPreAdapter", "coercion_lift_profile": "AggregateDirectAndRangeDualPolicy", "determinism_class": "Deterministic", "error_collapse_profile": "ReductionFold", "fec_dependency_profile": "None", "host_interaction_class": "None", "kernel_signature_class": "NumsToNum", "rich_value_usage": "RichBlind", "surface_fec_dependency_profile": "RefOnly", "thread_safety_class": "SafePure", "volatility_class": "NonVolatile" }, "descriptions": { "long": null, "short": "Smallest of the numbers", "short_source": "dna-calc-own" }, "docs": { "english_description": "Returns the minimum value in a list of arguments", "microsoft_url": "https://support.microsoft.com/en-us/office/min-function-61635d12-920f-4ce2-a70f-96f202dcc152" }, "entry_kind": "built_in_function", "localized_family_names": null, "localized_names": [ { "locale": "ar-SA", "name": "MIN" }, { "locale": "bg-BG", "name": "MIN" }, { "locale": "cs-CZ", "name": "MIN" }, { "locale": "da-DK", "name": "MIN" }, { "locale": "de-DE", "name": "MIN" }, { "locale": "el-GR", "name": "MIN" }, { "locale": "en-AU", "name": "MIN" }, { "locale": "en-GB", "name": "MIN" }, { "locale": "en-US", "name": "MIN" }, { "locale": "es-ES", "name": "MIN" }, { "locale": "et-EE", "name": "MIN" }, { "locale": "fi-FI", "name": "MIN" }, { "locale": "fr-FR", "name": "MIN" }, { "locale": "he-IL", "name": "MIN" }, { "locale": "hr-HR", "name": "MIN" }, { "locale": "hu-HU", "name": "MIN" }, { "locale": "id-ID", "name": "MIN" }, { "locale": "it-IT", "name": "MIN" }, { "locale": "ja-JP", "name": "MIN" }, { "locale": "ko-KR", "name": "MIN" }, { "locale": "lt-LT", "name": "MIN" }, { "locale": "lv-LV", "name": "MIN" }, { "locale": "nb-NO", "name": "MIN" }, { "locale": "nl-NL", "name": "MIN" }, { "locale": "pl-PL", "name": "MIN" }, { "locale": "pt-BR", "name": "MÍN" }, { "locale": "pt-PT", "name": "MIN" }, { "locale": "ro-RO", "name": "MIN" }, { "locale": "ru-RU", "name": "МИН" }, { "locale": "sk-SK", "name": "MIN" }, { "locale": "sl-SI", "name": "MIN" }, { "locale": "sr-Latn-RS", "name": "MIN" }, { "locale": "sv-SE", "name": "MIN" }, { "locale": "th-TH", "name": "MIN" }, { "locale": "tr-TR", "name": "MİN" }, { "locale": "uk-UA", "name": "MIN" }, { "locale": "vi-VN", "name": "MIN" }, { "locale": "zh-CN", "name": "MIN" }, { "locale": "zh-HK", "name": "MIN" }, { "locale": "zh-TW", "name": "MIN" } ], "signature": { "display": "MIN(number1, [number2], ...)", "parameters": [ { "description": null, "name": "number1", "optional": false, "repeats": false }, { "description": null, "name": "number2", "optional": true, "repeats": true } ], "trailing_repeats": true }, "surface_name": "MIN", "version_marker": null, "xlcall": { "code": "6", "symbol": "xlfMin" } }, "microsoft": "https://support.microsoft.com/en-us/office/min-function-61635d12-920f-4ce2-a70f-96f202dcc152" }, "try_it": { "formula": "=MIN(\"3\", 5)" }, "url": "https://handbook.dnacalc.com/functions/MIN.html", "variants": [], "versions": [ { "behaviour": "1,212 captured inputs are indexed for this environment. Capture dates: 2026-09-29 to 2026-09-29. This is a reading count, not a comparison with another build.", "excel_build": "16.0 build 20430", "platform": "Windows, 64-bit, CPU not recorded", "sources": [ "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.MIN.json" ] } ] }